Sum of the digits of a two-digit number is 9. When the digits are interchanged and 18 is subtracted from the new number, the resulting number is greater than the original number by 9. What is the two-digit number ?
Answers
Answer:
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Answer:
Let the unit place digit of a two-digit number be x.
Therefore, the tens place digit = 9-x
\because∵ 2-digit number = 10 x tens place digit + unit place digit
\therefore∴ Original number = 10(9-x)+x
According to the question, New number
= Original number + 27
\Rightarrow10x+\left(9-x\right)=10\left(9-x\right)+x+27⇒10x+(9−x)=10(9−x)+x+27
\Rightarrow10+9-x=90-10x+x+27⇒10+9−x=90−10x+x+27
\Rightarrow9x+9=117-9x⇒9x+9=117−9x
\Rightarrow9x+9x=117-9⇒9x+9x=117−9
\Rightarrow18x=108⇒18x=108
\Rightarrow x=\frac{108}{18}=6⇒x=
18
108
=6
Hence, the 2-digit number = 10(9-x)+x = 10(9-6)+6 = 10 x 3 + 6 = 30 + 6 = 36